Lect36_[Compatibility_Mode]

Lect36_[Compatibility_Mode] - Physics 344 Foundations of...

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Physics 344 Foundations of 21 st Century Physics: Relativity, Quantum Mechanics and heir Applications Their Applications Instructor: Dr. Mark Haugan Office: PHYS 282 haugan@purdue.edu TA: Dan Hartzler Office: PHYS 7 dhartzle@purdue.edu Grader: Shuo Liu Office: PHYS 283 liu305@purdue.edu Office Hours: If you have questions, just email us to make an ppointment. e enjoy talking about physics! appointment. We enjoy talking about physics! Reading: Six Ideas That Shaped Physics Unit Q, Chapters 7, 10 and 11 Notices:Midterm II at 8:00pm, Thursday, December 2 in MSEE B012
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Idealizing the Electron-Metal Film System We modeled the system consisting of a conduction electron interacting with the rest of the conducting film in which it is bound using a square potential well with depth determined by the workfunction of the conductor. 0, 0 () , 0 x Vx W x a < = −< < xa > The finite binding of this model allowed us to demonstrate that it is the condition that energy eigenstates of a system be normalizable that leads to the discrete energy spectrum characteristic of quantum bound states. For a solution of the time-independent Schrödinger equation to represent a state 2 2 ) () () E d x V x x ψ + = 2 2 E E Ex md x ψψ =+ the wavefunction Ψ E must fall off rapidly enough far from the well for * ) () f i n i t ev a l u e x d x e value E E xx −∞ = We saw why this is only possible for certain discrete values of the energy E .
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Our finite-square potential well model also revealed the distinctly quantum mechanical phenomenon of tunneling. The probability of detecting the electron in a classically rbidden region outside the metal film 3 () x ψ forbidden region outside the metal film is nonzero. Units in this figure put the film’s edges at x = 0 and 1. he relationship between a statevector and The relationship between a statevector and the probability density ρ (x) means that the probability of detecting the electron to the left of the well when the electron-film system is in the state Ψ 3 shown is 0 * 33 () () 0 xx d x ψψ −∞ > We’ve used the index 3 to label this state because the corresponding plot of the time-independent ρ (x) it implies has three “bumps”. Our discussion of the relationship between wavefunction “local wavelength” and particle kinetic energy indicates that this state will have more energy than the state with
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This note was uploaded on 11/26/2010 for the course PHYS 344 taught by Professor Garfinkel during the Spring '08 term at Purdue University-West Lafayette.

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Lect36_[Compatibility_Mode] - Physics 344 Foundations of...

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